Results 1 to 10 of about 516 (192)
Total Roman domination subdivision number in graphs [PDF]
Communications in Combinatorics and Optimization, 2020 A {\em Roman dominating function} on a graph $G$ is a function $f:V(G)\rightarrow \{0,1,2\}$ satisfying the condition that every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$.
Jafar Amjad
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On a conjecture concerning total domination subdivision number in graphs
AKCE International Journal of Graphs and Combinatorics, 2021 Let be the total domination number and let be the total domination subdivision number of a graph G with no isolated vertex. In this paper, we show that for some classes of graphs G, which partially solve the conjecture presented by Favaron et al.
S. Kosari +5 more
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On the total domination subdivision numbers in graphs
Open Mathematics, 2010 Abstract A set S of vertices of a graph G = (V, E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γ t(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number sdγt
Sheikholeslami Seyed
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Total $k$-rainbow domination subdivision number in graphs [PDF]
Computer Science Journal of Moldova, 2020 A total $k$-rainbow dominating function (T$k$RDF) of $G$ is a function $f$ from the vertex set $V(G)$ to the set of all subsets of the set $\{1,\ldots,k\}$ such that (i) for any vertex $v\in V(G)$ with $f(v)=\emptyset$ the condition $\bigcup_{u \in N(v ...
Rana Khoeilar +3 more
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Total dominator chromatic number of k-subdivision of graphs
The Art of Discrete and Applied Mathematics, 2022 Let $G$ be a simple graph. A total dominator coloring of $G$, is a proper coloring of the vertices of $G$ in which each vertex of the graph is adjacent to every vertex of some color class. The total dominator chromatic (TDC) number $ _d^t(G)$ of $G$, is the minimum number of colors among all total dominator coloring of $G$. For any $k \in \mathbb{N}$,
Alikhani, Saeid +2 more
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Total Domination Subdivision Number in Strong Product Graph [PDF]
American Journal of Applied Mathematics and Statistics, 2014 A set D of vertices in a graph G(V,E) is called a total dominating set if every vertex v∈V is adjacent to an element of D. The domination subdivision number of a graph G is the minimum number of edges that must be subdivided in order to increase the domination number of a graph. In this paper, we determine the total domination number for strong product
P. Jeyanthi, G. Hemalatha, B. Davvaz
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Total domination subdivision numbers of trees
Discrete Mathematics, 2004 The total domination subdivision number \(\text{ sd}_{\gamma_t}(G)\) of a graph \(G\) is the minimum number of edges whose subdivision increases the total domination number \({\gamma_t}(G)\) of \(G\). \textit{T. W. Haynes} et al. [J. Comb. Math. Comb. Comput.
Haynes, Teresa W. +2 more
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Total domination subdivision numbers of graphs
Discussiones Mathematicae Graph Theory, 2004 Summary: A set \(S\) of vertices in a graph \(G=(V,E)\) is a total dominating set of \(G\) if every vertex of \(V\) is adjacent to a vertex in \(S\). The total domination number of \(G\) is the minimum cardinality of a total dominating set of \(G\). The total domination subdivision number of \(G\) is the minimum number of edges that must be subdivided (
Haynes, Teresa W. +2 more
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Total Domination Multisubdivision Number of a Graph
Discussiones Mathematicae Graph Theory, 2015 The domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G.
Avella-Alaminos Diana +3 more
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Total domination and total domination subdivision number of a graph and its complement
Discrete Mathematics, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Favaron, O. +2 more
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